The Statistical Energy Analysis of Two Continuous One-Dimensional Subsystems

Abstract The ensemble average SEA of a system comprising two conservatively coupled subsystems is considered. Each subsystem is one dimensional in that it can support just one energy propagating wave. "Rain-on-the-roof" excitation acts on one subsystem and the excited subsystem is assumed to be uniform. The SEA hypothesis of coupling power proportionality is seen to be exact, irrespective of the strength of coupling. Four distinct strengths of coupling exist and two coupling parameters are found which govern the transitions between them. These parameters depend on the coupling reflection or transmission coefficient and the subsystem reflectances or modal overlaps. In weak coupling a small amount of power leaks from one subsystem to the other, while strong coupling is a case of energy sharing between the subsystems. There are also two forms of very strong coupling, namely re-radiation and re-injection coupling, in which one of the subsystems is relatively lightly damped and acts primarily as a store of energy. Exact expressions for the coupling power and coupling loss factor are found. These depend on the strength of coupling. The coupling loss factor depends additionally on an equipartition parameter which is significant when the coupling transmission coefficient is of the order of 1. The traditional wave estimate of coupling loss factor is seen to give a poor estimate except for subsystems which are weakly coupled and either reverberant or highly damped. Finally, applications to systems comprising a beam and a plate and to coupled beams are discussed.